1 Answer

Eulan · Answer 1 · 2023-12-03T05:28:24+0000

The given fraction is

We will multiply up and down by the conjugate of down (3 + i)

$\begin{gathered} (7+i)/(3-i)*(3+i)/(3+i)= \\ \\ ((7+i)(3+i))/((3-i)(3+i))= \\ \\ ((7)(3)+(7)(i)+(i)(3)+(i)(i))/((3)(3)-(i)(i))= \end{gathered}$

Add the like terms

$\begin{gathered} (21+7i+3i+i^2)/(9-i^2)= \\ \\ (21+10i-1)/(9-(-1))= \\ \\ (20+10i)/(9+1)= \\ \\ (20+10i)/(10) \end{gathered}$

Take 10 as a common factor from up

$\begin{gathered} (10(2+i))/(10)= \\ \\ 2+i \end{gathered}$

The answer is C

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